SOLUTION: the sum of three numbers is 95 the sum of the first and the second is twenty-five more than the third number and the third is twice the first. find the numbers and show your work.

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Question 234666: the sum of three numbers is 95 the sum of the first and the second is twenty-five more than the third number and the third is twice the first. find the numbers and show your work. i know this problem is x+y+z=95 but then I dont know where to go from there.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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he sum of three numbers is 95 the sum of the first and the second is twenty-five more than the third number and the third is twice the first.
find the numbers and show your work. i know this problem is x+y+z=95
but then I dont know where to go from there.
Going on from there
:
"the sum of three numbers is 95."
x + y + z = 95
;
" the sum of the first and the second is twenty five more than the third number
x + y = z + 25
:
" the third is twice the first."
z = 2x
:
find the numbers.
:
rewrite the 2nd equation and subtract from the 1st equaion
x + y + z = 95
x + y - z = 25
-----------------subtraction eliminates x and y, find z
2z = 70
z = 35
therefore
2x = 35
x = 17.5
:
Find y, using the 2nd equation:
17.5 + y = 35 + 25
y = 60 - 17.5
y = 42.5
;
:
Check the sum of the three numbers
17.5 + 42.5 + 35 = 95